A note on quadratic forms
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2023
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866914668526698496 |
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| author | Hebestreit, Fabian Krause, Achim Ramzi, Maxime |
| author_facet | Hebestreit, Fabian Krause, Achim Ramzi, Maxime |
| contents | For a field extension $L/K$ we consider maps that are quadratic over $L$ but whose polarisation is only bilinear over $K$. Our main result is that all such are automatically quadratic forms over $L$ in the usual sense if and only if $L/K$ is formally unramified. In particular, this shows that over finite and number fields, one of the axioms in the standard definition of quadratic forms is superfluous. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_01795 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A note on quadratic forms Hebestreit, Fabian Krause, Achim Ramzi, Maxime Commutative Algebra K-Theory and Homology For a field extension $L/K$ we consider maps that are quadratic over $L$ but whose polarisation is only bilinear over $K$. Our main result is that all such are automatically quadratic forms over $L$ in the usual sense if and only if $L/K$ is formally unramified. In particular, this shows that over finite and number fields, one of the axioms in the standard definition of quadratic forms is superfluous. |
| title | A note on quadratic forms |
| topic | Commutative Algebra K-Theory and Homology |
| url | https://arxiv.org/abs/2308.01795 |